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Fermions in a infinite 1D well and spinorbital

I am learning quantum chemistry. To have a comprehensive understanding of the Slater determinant, I studied the classical problem of two indistinguishable particles in a 1D box with infinite barriers. ...
Stef1611's user avatar
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What are some good references for periodic Hartree-Fock calculations?

I am looking to implement a Hartree-Fock program to study periodic, condensed matter system, however, I literally cannot find a single reference or example anywhere for how to do this. In the past, I ...
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1 answer
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Other than approximating the total energy of the system, what other information does the Hartree-Fock method provide?

In the Hartree-Fock method, one computes the energy of an interacting quantum-many body system, described by $H$, via taking a non-interacting trial ground state, $|\psi_{\mathrm{HF}}\rangle$, and ...
meer23's user avatar
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2 votes
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Could the scattering of molecules lead to bond compression?

Suppose you were to send a fast moving binary molecule (such as H-H) at another large target atom A such that the molecule is aligned with the direction of its travel towards the target atom. In other ...
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27 views

Boron triplet states

Is it possible to achieve the following electron configuration of triplets in Boron, if you were to align the spins by means of electric field, or magnetic field, or just electromagnetic radiation? [!...
Jais's user avatar
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Difference between GW gap and BSE gap. How does net charge play a role?

The energy gap from BSE (GW-BSE) is just the lowest optical excitation energy. The energy gap from GW, from what I read, is the electron affinity (energy of adding an electron). I suppose this means ...
Bohan Xu's user avatar
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Total ground state energy calculation of an electron-ion system using plane wave basis sets

Recently I have begun working on a project which involves constructing a "simple" density functional theory (DFT) code using a plane wave basis set in Python. My first step has been to try ...
m.roussev's user avatar
3 votes
1 answer
85 views

Can Hartree-Fock determinant WLOG taken to be real?

For a many-electron Hamiltonian $H$, a Hartree-Fock determinant is a Slater determinant $\Psi$ that minimizes the energy $\frac{\langle\Psi,H\Psi\rangle}{\langle\Psi,\Psi\rangle}$. In general, $\Psi$ ...
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Flatband with our Moire Physics

Is there any material Class available where the lattice vectors are in the order of several nm instead of Angstrom? I am looking for some exotic not well studies lattice class which can be ...
Rockey's user avatar
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Why ionization energy of oxygen dips moving from nitrogen to oxygen if the total spin decreased?

How does spin-orbit splitting also affect this or anomalous zeeman effect or decrease in spin when you move from Nitrogen to Oxygen? Bad Teacher: The addition of the second electron into an already ...
jkj's user avatar
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Placement of nucleons in the shell model for odd-even nuclei

The question I'm trying to answer is this: What are the spin and parity predicted by the shell model for 37 20Ca (in order of increasing energy the order of states is [1s1/2 , 1p3/2 , 1p1/2 ][1d5/2 , ...
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Conflicts on spin directions in the molecular term symbol for O$_2$

We know that the ground-state electron configuration of O$_2$ is $K K (\sigma_g 2s)^2 (\sigma_u 2s)^2 (\sigma_g 2p_z)^2 (\pi_u 2p_x)^2 (\pi_u 2p_y)^2 (\pi_g 2p_x)^1 (\pi_g 2p_y)^1$. The spins of the ...
ranger's user avatar
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0 answers
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Muonic Hydrogen Dissociation

Is the dissociation energy of a muonic molecular hydrogen ion the same as an ordinary molecular hydrogen ion? Would the cross-section for dissociation be the same as an ordinary molecular hydrogen ion?...
S.T. Zweig's user avatar
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28 views

Exchange Particles for IMF

Quantum field theory describes forces as being mediated by a field (e.g. gluon field for strong force, electromagnetic field for electromagnetic force). These are often modeled as a mediating boson ...
18th Shard's user avatar
2 votes
1 answer
106 views

How to calculate total angular momentum $L$ of partially filled $p$-orbitals?

Why has $^1D$ configuration lower energy than $^1S$ ? Hund's second rule says that for two configurations with the same multiplicity, the configuration with the highest total orbital angular momentum $...
MichaelW's user avatar
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3 votes
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What is the relation between the Adiabatic Approximation used in quantum chemistry and the one given in QM textbooks?

I am an aspiring quantum chemist and have come across two vastly different versions of the Adiabatic Approximation when studying Quantum Mechanics from the perspective of physics and chemistry ...
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Angular momentum uncertainty principle and the particle on a ring

By considering a particle on a ring, the eigenfunctions of $H$ are also eigenfunctions of $L_\text{z}$: $$\psi(\phi) = \frac{1}{\sqrt{2\pi}}e^{im\phi}$$ with $m = 0,\pm 1,\pm 2,\cdots$. In polar ...
Physical Chemist's user avatar
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68 views

Carbon dioxide vibration

Can we induce antisymmetric stretching vibration in carbon dioxide molecules by collision with nitrogen molecules in air at standard temperature and pressure?
Stan Tarka's user avatar
4 votes
1 answer
139 views

The relation between state function and molecular orbitals

In some chemistry classes I was taught the (seemingly usual) 'tale of exactly two atoms' that form bonding and anti-bonding states in the LCAO-theory (similar to this question). I've not seen the ...
Mikkel Rev's user avatar
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1 answer
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Thermodynamics and Gibbs energy

The equation for the Gibbs free energy is: $\Delta G = \Delta H - T\Delta S.$ $\Delta H$ is the amount of energy difference between the initial state (characterized by $U_{i}$, $S_{i}$, and $V_{i}$) ...
15_7008 Phú Hữu Trần Đôn's user avatar
1 vote
2 answers
98 views

How is energy conserved in formation of chemical bonds?

I understand that when an H$_2$O molecule is formed, it has lesser total energy than the constituent (2H and O) atoms. I also understand that the potential energy (PE) will be reduced when the atoms ...
Alex's user avatar
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0 answers
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Measurement of dipole electric field generated by a polar molecule

I'm trying to understand the nature of polar molecules. Have there been experiments where we can say to have actually measured the dipole electric field generated by a polar molecule such as hydrogen ...
Rudyard's user avatar
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Is Hartree-Fock energy minimisation an iterative or a Lagrange undetermined process?

Suppose the following is about a quantum system of N electrons. In the canonical Hartree-Fock method, the goal is to find single - electron orbitals $\phi_{1}, ...,\phi_{N}$ such that $\langle \psi_{...
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1 answer
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Number of summations for a Hartree-Fock (single-orbital as basis functions) method

The Hamiltonian for a quantum $N$ - body system: $$\hat{H} = - \frac{1}{2}\sum_{i}^{N}\nabla_{i}^{2}-\sum_{m;i=1}^{N}\frac{z_{m}}{r_{im}}+ \sum_{i;j>i}\frac{1}{r_{ij}}.$$ The first two terms can be ...
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3 votes
0 answers
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Can a matter enter do work without being consumed up? [closed]

I had a tricky question in mind. So, I wanted to use the example of Catalysts (In chemical reactions) as an example. It's said that when catalysts enter a chemical reaction, they're Never consumed up. ...
AMA's user avatar
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1 vote
1 answer
160 views

Where is the kinetic energy functional error in the exchange-correlation functional of DFT?

The Kohn-Sham DFT energy functional is: $$E[\rho]=T^S[{\varphi_i}]+J[\rho]+M[\rho]+E^{xc}[\rho]$$ with the kinetic energy functional of non-interacting electrons $T^S$, the Hartree functional $J$, the ...
Guiste's user avatar
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2 votes
2 answers
234 views

Why using real wave functions instead of complex ones?

I have already seen similar questions asked in the site (like this or this), but I don't feel that my question has been fully addressed. I understand that orbitals $np_x$ and $np_y$ are linear ...
efrenump's user avatar
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2 votes
0 answers
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On completeness of a set of commuting operators for homonuclear diatomic molecules

The electronic Hamiltonian for a homonuclear diatomic molecule is $$\hat{H}=-\sum_{i=1}^N \frac{\hbar^2}{2m} \nabla^2_i -\sum_{i=1}^N \frac{Z_Ae^2}{4\pi\epsilon_0|\vec{r}_i-\vec{R}_A|} -\sum_{i=1}^N \...
Simone's user avatar
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8 votes
3 answers
936 views

Density functional theory: logical steps from Hohenberg-Kohn theorems to Kohn-Sham equations

I'm trying to learn density functional theory (DFT), using Engel & Dreisler, Sholl & Steckel, and Wikipedia as 3 different sources of information. Although I have made some progress, I am ...
Kenny Wong's user avatar
1 vote
3 answers
64 views

Deducing physical properties of substances with physics

Inspired by this question (Why does amount of protons define how matter is?) I’m wondering how one can deduce the physical properties of an element with physics. For example, it is known that sodium ...
user avatar
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0 answers
44 views

Gibbs energy calculations for compounds

I am studying machine learning during my master's degree and have a simple task. I am using the FactSage Pure Substance Database (https://www.crct.polymtl.ca), which provides a list of phases for a ...
1 vote
0 answers
91 views

Is it possible to calculate the average kinetic energy of an atomic orbital in an heavy atom? [closed]

I am trying to calculate cross sections for electron impact ionization in heavy atoms (Xe and I) using a BEB technique. To do this I need, for each occupied orbital, occupancy number, binding energy ...
FBianchi98's user avatar
4 votes
1 answer
156 views

What is the physical origin of two Hydrogen atoms repelling at short distance?

Consider two isolated $\rm H$ atoms. They can be in different spin states, but the different states are degenerate. Now move these $\rm H$ atoms together. Now the singlet state will become ...
Guiste's user avatar
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3 votes
2 answers
123 views

Where does this (hydrogen molecule energy) graph come from?

I was thinking about the good old question of 'Why do molecules have lower energy than the atoms?' And in a video (around 6:15), this good old energy graph is shown, which is stated as the 'answer' to ...
Rohit Shekhawat's user avatar
-2 votes
1 answer
163 views

Dirac equation for solving $\rm H^-$ anion

Let's try to solve 1 dimensional Dirac equation for a $\rm H^-$ anion. If you solve the time independent Dirac equation and allow motion of electrons only in the $x$ axis you get: $$-\chi\frac{d\Psi_{...
appliedSciences's user avatar
1 vote
0 answers
20 views

How do nuclear physicists know for certain if a very short-lived nucleus has been formed (a new isotope)?

Some very short-lived nuclides (sometimes called 'resonances') are nevertheless considered to have actually existed, if only very very briefly.... How do nuclear physicists know the isotope actually ...
Kurt Hikes's user avatar
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1 vote
1 answer
313 views

Why does Fock operator in Hartree-Fock method have the molecule symmetry?

I am reading Szabo - 1967 - Modern Quantum Chemistry. In Chapter 3 P122, it mentions that the spin orbitals $\left|\chi_a\right\rangle$ obtained by the Fock operator $f\left|\chi_a\right\rangle=\...
Zharip's user avatar
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2 votes
1 answer
739 views

How is the band gap really defined and calculated?

When I look into literature I am quite confused on how the band gap of a semiconductor is defined. One statement I often read goes something like that: The band gap of a semiconductor is the energy ...
Lockhart 's user avatar
2 votes
0 answers
232 views

How do I interpret the single electron Hamiltonian contribution in the Roothan-Hall equation?

I am currently going through Molecular Modelling: Principles and Applications by Andrew R. Leach (2nd Edition). The Hamiltonian operator for an electron is given in equation (2.125) as $$\mathscr{H}^{...
VinalV's user avatar
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2 votes
0 answers
62 views

Quantum simulation of molecular spectroscopy: why?

Molecular spectroscopy, e.g. through light-matter interaction, is a powerful tool to measure molecular properties such as bond lengths, energy levels, vibration frequencies, ... which give insights ...
m137's user avatar
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1 vote
0 answers
44 views

Can you burn a quantum fluid?

Perhaps more generally, can you have a chemical reaction between a quantum fluid (a sodium Bose-Einstein condensate for example) and another quantum fluid or a non-quantum fluid? Or as a silly ...
SarahJuliet1510's user avatar
7 votes
2 answers
672 views

Is Hartree-Fock (HF) a ground state theory?

To calculate the orbitals in Hartree-Fock (HF) theory we imply the variations principle, so we try to find the wavefunction which minimises the energy $\left<\psi|H|\psi\right>$. This ...
Lockhart 's user avatar
11 votes
2 answers
1k views

Why does Hartree-Fock (HF) theory even work?

Let’s say we have $N$ electrons and we want to derive the Hartree-Fock (HF) equations. The first step would be to define a Slater determinant of $N$ electrons: $$\psi(x_1,x_2,… x_N) = \frac{1}{\sqrt{...
Lockhart 's user avatar
4 votes
2 answers
230 views

From molecular orbitals to band diagram

Let’s say we have a periodic crystal structure. We could, in theory, treat this system as if it were a large molecule. Therefore, we could use Hartree Fock theory or other methods to get the molecular ...
Lockhart 's user avatar
3 votes
1 answer
207 views

Why is there no exchange interaction when there is no coulomb interaction?

The Hartree-Fock energy may be written as $$ E_{HF}= \langle\Psi| H |\Psi\rangle = \sum_{a} \langle a| h |a \rangle + \frac{1}{2}\sum_{ab} \big( [aa |bb] - [ab|ba] \big),$$ with the exchange term $$[...
Lockhart 's user avatar
0 votes
1 answer
238 views

General form of a fermionic Hamiltonian in second quantization

I am a new to quantum chemistry. I've been reading this paper and it seems like the equation (1) in the paper which is, $H = \sum_{pq} T_{pq} a_p^\dagger a_q + \sum_p U_pn_p + \sum_{pq} V_{pq} n_p n_q$...
userflux9674's user avatar
3 votes
0 answers
184 views

Ammonia electric dipole moment according to Philip Warren Anderson

In his paper "More is Different", Philip Warren Anderson claims to be in posession of a proof by which any stationary state of an Ammonia molecule (or anything really, again according to him,...
GoingWeb's user avatar
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1 answer
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What is the reason for Avagadro's Law?

From outside the quantum stuff I'm tiredelessly learning, I've been reminded about Avagadro's Law — i.e., the fact that any molecular gas has the same count of molecules in the same volume and ...
Victor Novak's user avatar
1 vote
0 answers
162 views

Potential Energy of the Helium Atom

So I just learned how to solve the Schroedinger Equation for the Hydrogen atom. The set up looked like this: $$\left[\dfrac{1}{r^2}\frac{\partial}{\partial r}\left(r^2\dfrac{\partial}{\partial r}\...
Kamal Saleh's user avatar
1 vote
0 answers
90 views

How did the Aufbau principle come to be? [duplicate]

How did the Aufbau principle come to be? Being that my education on chemistry doesn't go past highschool, i was never sure how the following diagram was conceived: I would like to understand how the ...
P. Nobre's user avatar

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